@book{HATCHER,
    abstract = {
This book is one of the most interesting and
accessible texts to come out in recent years. The subject is presented in
three broad areas: elementary notions including fundamental group, homology
and cohomology, and homotopy theory. In most cases, some of the more
sophisticated topics, such as \$H\$-spaces, Bockstein homomorphisms and Hopf
invariants, are placed in sections called "Additional Topics" at the end
of the appropriate chapter.
<P>
The style is refreshingly informal, although precise definitions are always
given. The author always prepares the reader for the next idea, and there
are basic, simple black and white pictures which really help. He is not
afraid to repeat ideas with increasing generality. For example, there are
treatments of Postnikov towers which begin with a cellular version, go on
to the usual tower of principal fibrations and end with Moore-Postnikov
decompositions. The reviewer finds this a very "student-friendly"
approach (very different from the texts which always look for the greatest
generality). There are many excellent examples.
<P>
The author talks about two further volumes involving spectral sequences and
\$K\$-theory. When complete, this will be a major achievement which will help a
great many serious students.},
    address = {Cambridge},
    author = {Hatcher, Allen},
    citeulike-article-id = {471863},
    citeulike-linkout-0 = {http://www.ams.org/mathscinet-getitem?mr=1867354},
    keywords = {algebraic\_topology, textbook},
    mrnumber = {MR1867354},
    posted-at = {2006-01-20 02:18:54},
    priority = {2},
    publisher = {Cambridge University Press},
    title = {Algebraic topology},
    url = {http://www.ams.org/mathscinet-getitem?mr=1867354},
    year = {2002}
}

@book{Munkres,
    author = {Munkres, James R.},
    citeulike-article-id = {1847989},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0201627280},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0201627280},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0201627280},
    citeulike-linkout-3 = {http://www.amazon.co.uk/exec/obidos/ASIN/0201627280/citeulike00-21},
    citeulike-linkout-4 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0201627280},
    citeulike-linkout-5 = {http://www.worldcat.org/isbn/0201627280},
    citeulike-linkout-6 = {http://books.google.com/books?vid=ISBN0201627280},
    citeulike-linkout-7 = {http://www.amazon.com/gp/search?keywords=0201627280&index=books&linkCode=qs},
    citeulike-linkout-8 = {http://www.librarything.com/isbn/0201627280},
    day = {01},
    howpublished = {Paperback},
    isbn = {0201627280},
    keywords = {algebra, topology},
    month = {December},
    posted-at = {2007-10-31 17:41:00},
    priority = {2},
    publisher = {{Westview Press}},
    title = {Elements of Algebraic Topology},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0201627280},
    year = {1993}
}

@book{Maclane,
    author = {Mac Lane, Saunders},
    edition = {3rd},
    month = {October},
    posted-at = {2008-12-04 10:45:49},
    priority = {2},
    publisher = {Springer},
    title = {Homology},
    year = {1975}
}

@book{Weibel,
    abstract = {The landscape of homological algebra has evolved over the past half-centuryinto a fundamental tool for the working mathematician. This book provides aunified account of homological algebra as it exists today. The historicalconnection with topology, regular local rings, and semi-simple Lie algebras isalso described. The first half of the book takes as its subject the canonicaltopics in homological algebra: derived functors, Tor and Ext, projectivedimensions and spectral sequences. Homology of group and Lie algebrasillustrate these topics. Intermingled are less canonical topics, such as thederived inverse limit functor lim1, local cohomology, Galois cohomology, andaffine Lie algebras. The last part of the book covers less traditional topicsthat are a vital part of the modern homological toolkit: simplicial methods,Hochschild and cyclic homology, derived categories and total derived functors.},
    author = {Weibel, Charles A.},
    citeulike-article-id = {5099114},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0521559871},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0521559871},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0521559871},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0521559871},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0521559871/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0521559871},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0521559871},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0521559871},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0521559871&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0521559871},
    day = {27},
    howpublished = {Paperback},
    isbn = {0521559871},
    keywords = {homological\_algebra},
    month = {October},
    posted-at = {2009-07-09 22:01:28},
    priority = {2},
    publisher = {Cambridge University Press},
    title = {An Introduction to Homological Algebra},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0521559871},
    year = {1995}
}

@book{Rotman,
    abstract = {With a wealth of examples as well as abundant applications to algebra, this is a must-read work: an easy-to-follow, step-by-step guide to homological algebra. The author provides a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added. Applications include the following: * to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings, Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique factorization); * to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsion groups; * to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over compact Riemann surfaces. Learning homological algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, and what this describes. Secondly, one must be able to compute these things using a separate language: that of spectral sequences. The basic properties of spectral sequences are developed using exact couples. All is done in the context of bicomplexes, for almost all applications of spectral sequences involve indices. Applications include Grothendieck spectral sequences, change of rings, Lyndon-Hochschild-Serre sequence, and theorems of Leray and Cartan computing sheaf cohomology.},
    author = {Rotman, Joseph J.},
    citeulike-article-id = {3745334},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0387245278},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0387245278},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0387245278},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0387245278},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0387245278/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0387245278},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0387245278},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0387245278},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0387245278&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0387245278},
    day = {14},
    edition = {2nd},
    howpublished = {Paperback},
    isbn = {0387245278},
    keywords = {homological\_algebra},
    month = {October},
    posted-at = {2008-12-04 10:45:49},
    priority = {2},
    publisher = {Springer},
    title = {An Introduction to Homological Algebra},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0387245278},
    year = {2008}
}

@book{Lang,
    abstract = {{"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." \&nbsp;NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."\&nbsp;MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. \&nbsp;For the revised third edition, the author has added exercises and made numerous corrections to the text.}},
    author = {Lang, Serge},
    citeulike-article-id = {117768},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/038795385X},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/038795385X},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/038795385X},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/038795385X},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/038795385X/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/038795385X},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/038795385X},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN038795385X},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=038795385X&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/038795385X},
    day = {08},
    howpublished = {Hardcover},
    isbn = {038795385X},
    keywords = {algebra},
    month = {January},
    posted-at = {2005-03-09 14:27:50},
    priority = {2},
    publisher = {Springer},
    title = {Algebra},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/038795385X},
    year = {2002}
}

@book{Dummit_Foote,
    abstract = {Widely acclaimed algebra text. This book is designed to give the reader
insight into the power and beauty that accrues from a rich interplay between
different areas of mathematics. The book carefully develops the theory of
different algebraic structures, beginning from basic definitions to some in-
depth results, using numerous examples and exercises to aid the reader's
understanding. In this way, readers gain an appreciation for how mathematical
structures and their interplay lead to powerful results and insights in a
number of different settings.

* The emphasis throughout has been to motivate the introduction and
development of important algebraic concepts using as many examples as
possible.},
    author = {Dummit, David S. and Foote, Richard M.},
    citeulike-article-id = {3349424},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0471433349},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0471433349},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0471433349},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0471433349},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0471433349/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0471433349},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0471433349},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0471433349},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0471433349&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0471433349},
    day = {14},
    edition = {3},
    howpublished = {Hardcover},
    isbn = {0471433349},
    keywords = {algebra, book},
    month = {July},
    posted-at = {2008-09-29 01:56:05},
    priority = {2},
    publisher = {Wiley},
    title = {Abstract Algebra},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0471433349},
    year = {2003}
}

@book{CLR,
    abstract = {Aimed at any serious programmer or computer science student, the new second edition of \_Introduction to Algorithms\_ builds on the tradition of the original with a truly magisterial guide to the world of algorithms. Clearly presented, mathematically rigorous, and yet approachable even for the maths- averse, this title sets a high standard for a textbook and reference to the best algorithms for solving a wide range of computing problems. With sample problems and mathematical proofs demonstrating the correctness of each algorithm, this book is ideal as a textbook for classroom study, but its reach doesn't end there. The authors do a fine job at explaining each algorithm. (Reference sections on basic mathematical notation will help readers bridge the gap, but it will help to have some maths background to appreciate the full achievement of this handsome hardcover volume.) Every algorithm is presented in pseudo-code, which can be implemented in any computer language, including C/C++ and Java. This ecumenical approach is one of the book's strengths. When it comes to sorting and common data structures, from basic linked list to trees (including binary trees, red-black and B-trees), this title really shines with clear diagrams that show algorithms in operation. Even if you glance over the mathematical notation here, you can definitely benefit from this text in other ways. The book moves forward with more advanced algorithms that implement strategies for solving more complicated problems (including dynamic programming techniques, greedy algorithms, and amortised analysis). Algorithms for graphing problems (used in such real-world business problems as optimising flight schedules or flow through pipelines) come next. In each case, the authors provide the best from current research in each topic, along with sample solutions. This text closes with a grab bag of useful algorithms including matrix operations and linear programming, evaluating polynomials and the well-known Fast Fourier Transformation (FFT) (useful in signal processing and engineering). Final sections on "NP-complete" problems, like the well-known traveloling salesmen problem, show off that while not all problems have a demonstrably final and best answer, algorithms that generate acceptable approximate solutions can still be used to generate useful, real-world answers. Throughout this text, the authors anchor their discussion of algorithms with current examples drawn from molecular biology (like the Human Genome project), business, and engineering. Each section ends with short discussions of related historical material often discussing original research in each area of algorithms. In all, they argue successfully that algorithms are a "technology" just like hardware and software that can be used to write better software that does more with better performance. Along with classic books on algorithms (like Donald Knuth's three-volume set, \_The Art of Computer Programming\_), this title sets a new standard for compiling the best research in algorithms. For any experienced developer, regardless of their chosen language, this text deserves a close look for extending the range and performance of real-world software. \_--Richard Dragan\_},
    author = {Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford},
    citeulike-article-id = {3395496},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0072970545},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0072970545},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0072970545},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0072970545},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0072970545/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0072970545},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0072970545},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0072970545},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0072970545&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0072970545},
    edition = {2nd},
    howpublished = {Hardcover},
    isbn = {0072970545},
    keywords = {books, cormen, introduction-to-algorithms, reference},
    month = {December},
    posted-at = {2009-01-06 13:45:29},
    priority = {2},
    publisher = {McGraw-Hill Science / Engineering / Math},
    title = {Introduction to Algorithms},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0072970545},
    year = {2003}
}

@article{Carlsson_09,
    author = {Carlsson, Gunnar},
    journal = {Bulletin of the American Mathematical Society},
    volume = {46},
    number = {2},
    pages = {255-308},
    year = {2009},
    citeulike-article-id = {5173472},
    citeulike-linkout-0 = {http://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/home.html},
    keywords = {geometry, learning\_theory, topology, viaarthegall},
    posted-at = {2009-07-16 22:36:31},
    priority = {4},
    title = {{Topology and data}},
    url = {http://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/home.html}
}

@book{Statistical_Learning,
    abstract = {During the past decade there has been an explosion in computation and
information technology. With it has come vast amounts of data in a variety of
fields such as medicine, biology, finance, and marketing. The challenge of
understanding these data has led to the development of new tools in the field
of statistics, and spawned new areas such as data mining, machine learning,
and bioinformatics.

Many of these tools have common underpinnings but are often expressed with
different terminology. This book describes the important ideas in these areas
in a common conceptual framework. While the approach is statistical, the
emphasis is on concepts rather than mathematics. Many examples are given, with
a liberal use of color graphics. It should be a valuable resource for
statisticians and anyone interested in data mining in science or industry.

The book's coverage is broad, from supervised learning (prediction) to
unsupervised learning. The many topics include neural networks, support vector
machines, classification trees and boosting--the first comprehensive treatment
of this topic in any book.

Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of
statistics at Stanford University. They are prominent researchers in this
area: Hastie and Tibshirani developed generalized additive models and wrote a
popular book of that title. Hastie wrote much of the statistical modeling
software in S-PLUS and invented principal curves and surfaces. Tibshirani
proposed the Lasso and is co-author of the very successful An Introduction to
the Bootstrap. Friedman is the co-inventor of many data-mining tools including
CART, MARS, and projection pursuit.

FROM THE REVIEWS:

TECHNOMETRICS "[This] is a vast and complex book. Generally, it concentrates
on explaining why and how the methods work, rather than how to use them.
Examples and especially the visualizations are principle features...As a
source for the methods of statistical learning...it will probably be a long
time before there is a competitor to this book."},
    author = {Hastie, T. and Tibshirani, R. and Friedman, J. H.},
    citeulike-article-id = {161814},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0387952845},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0387952845},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0387952845},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0387952845},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0387952845/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0387952845},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0387952845},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0387952845},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0387952845&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0387952845},
    edition = {Corrected},
    howpublished = {Hardcover},
    isbn = {0387952845},
    keywords = {learning, statistical},
    month = {July},
    posted-at = {2006-09-07 14:05:31},
    priority = {4},
    publisher = {Springer},
    title = {The Elements of Statistical Learning},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0387952845},
    year = {2003}
}


@article{Carlsson_04,
    abstract = {We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This results generalizes and extends the previously known algorithm that was restricted to subcomplexes of S},
    author = {Zomorodian, Afra and Carlsson, Gunnar},
    citeulike-article-id = {3148973},
    citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064},
    journal = {Discrete Comput. Geom},
    keywords = {cleaning},
    pages = {249--274},
    posted-at = {2008-08-22 13:33:55},
    priority = {2},
    title = {Computing Persistent Homology},
    url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064},
    volume = {33},
    year = {2005}
}

@book{Boyd,
    abstract = {{Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.}},
    author = {Boyd, Stephen and Vandenberghe, Lieven},
    citeulike-article-id = {163662},
    citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/0521833787},
    citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/0521833787},
    citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/0521833787},
    citeulike-linkout-3 = {http://www.amazon.jp/exec/obidos/ASIN/0521833787},
    citeulike-linkout-4 = {http://www.amazon.co.uk/exec/obidos/ASIN/0521833787/citeulike00-21},
    citeulike-linkout-5 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0521833787},
    citeulike-linkout-6 = {http://www.worldcat.org/isbn/0521833787},
    citeulike-linkout-7 = {http://books.google.com/books?vid=ISBN0521833787},
    citeulike-linkout-8 = {http://www.amazon.com/gp/search?keywords=0521833787&index=books&linkCode=qs},
    citeulike-linkout-9 = {http://www.librarything.com/isbn/0521833787},
    comment = {a must read for convex optimization which is essentially important for optimization theory: an underlying techinique for solving SVM.

Contains theory, applicatoins, algorithms.},
    day = {08},
    howpublished = {Hardcover},
    isbn = {0521833787},
    keywords = {convex, optimization},
    month = {March},
    posted-at = {2005-04-18 20:01:17},
    priority = {4},
    publisher = {Cambridge University Press},
    title = {Convex Optimization},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0521833787},
    year = {2004}
}

@inproceedings{de_Silva_Johansson,
 author = {de Silva, Vin and Vejdemo-Johansson, Mikael},
 title = {Persistent cohomology and circular coordinates},
 booktitle = {SCG '09: Proceedings of the 25th annual symposium on Computational geometry},
 year = {2009},
 isbn = {978-1-60558-501-7},
 pages = {227--236},
 location = {Aarhus, Denmark},
 doi = {http://doi.acm.org/10.1145/1542362.1542406},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@inproceedings{Witness,
    author = {de Silva, Vin and Carlsson, Gunnar},
    booktitle = {Eurographics Symposium on Point-Based Graphics},
    citeulike-article-id = {3148971},
    citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/showciting?cid=162914},
    editor = {Alexa, M. and Rusinkiewicz, S.},
    keywords = {cleaning},
    organization = {The Eurographics Association},
    posted-at = {2008-08-22 13:33:21},
    priority = {2},
    title = {{Topological estimation using witness complexes}},
    url = {http://citeseerx.ist.psu.edu/showciting?cid=162914},
    year = {2004}
}


@inproceedings{Mapper,
author = {Gurjeet Singh and Facundo Memoli and Gunnar Carlsson },
title = {{Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition}},
pages = {91-100},
URL = {http://www.eg.org/EG/DL/WS/SPBG/SPBG07/091-100.pdf},
DOI = {10.2312/SPBG/SPBG07/091-100},
abstract = {We present a computational method for extracting simple descriptions of high dimensional data sets in the form of simplicial complexes. Our method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data. The proposed method is not dependent on any particular clustering algorithm, i.e. any clustering algorithm may be used with Mapper. We implement this method and present a few sample applications in which simple descriptions of the data present important information about its structure.}
}

@ARTICLE{mumford,
    author = {Gunnar Carlsson and Tigran Ishkhanov and Vin De Silva and Afra Zomorodian},
    title = {On the local behavior of spaces of natural images},
    journal = {Internat. J. Comput. Vision},
    year = {2006},
    volume = {2007}
}

@article{Zomorodian,
  author = "Zomorodian, A.", 
  title = "Fast Construction of the {V}ietoris-{R}ips Complex",
  journal = "Computers \& Graphics", 
  year = 2010,
  volume = 34,
  number = 3,
  pages = "263 -- 271",
  doi = "doi:10.1016/j.cag.2010.03.007",
}

@misc{Dualities,
    author = {de Silva, Vin and Morozov, Dmitriy and Vejdemo-Johansson, Mikael},
    citeulike-article-id = {7349266},
    citeulike-linkout-0 = {http://math.stanford.edu/%7Emik/papers/4corners.pdf},
    citeulike-linkout-1 = {http://math.stanford.edu/~mik/papers/4corners.pdf},
    howpublished = {Unpublished manuscript},
    keywords = {computational-topology},
    posted-at = {2010-06-22 17:28:22},
    priority = {2},
    title = {{Dualities in persistent (co)homology}},
    url = {http://math.stanford.edu/%7Emik/papers/4corners.pdf},
    year = {2010}
}

@article {ELZ_02,
    AUTHOR = {Edelsbrunner, Herbert and Letscher, David and Zomorodian,
              Afra},
     TITLE = {Topological persistence and simplification},
      NOTE = {Discrete and computational geometry and graph drawing
              (Columbia, SC, 2001)},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {28},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {511--533},
      ISSN = {0179-5376},
     CODEN = {DCGEER},
   MRCLASS = {52B55 (65D18)},
  MRNUMBER = {1949898 (2003m:52019)},
MRREVIEWER = {H. W. Guggenheimer},
       DOI = {10.1007/s00454-002-2885-2},
       URL = {http://dx.doi.org/10.1007/s00454-002-2885-2},
}

@misc{hom,
    author = {Tausz, Andrew and Carlsson, Gunnar},
    howpublished = {Preprint},
    keywords = {computational-topology},
    priority = {2},
    title = {{Homological Coordinatization}},
    url = {http://www.stanford.edu/%7Eatausz/homological_coordinatization.pdf},
    year = {2011}
}
	
